Related papers: A Second Law for Open Markov Processes
We investigate the fundamental relation between entropy production rate and the speed of energy exchange between a system and baths in classical Markov processes. We establish the fact that quick energy exchange inevitably induces large…
We seek to infer the parameters of an ergodic Markov process from samples taken independently from the steady state. Our focus is on non-equilibrium processes, where the steady state is not described by the Boltzmann measure, but is…
In this paper we present elementary computations for some Markov modulated counting processes, also called counting processes with regime switching. Regime switching has become an increasingly popular concept in many branches of science. In…
Stochastic thermodynamics and the associated fluctuation relations provide the means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually…
We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…
It is a common belief that in any environment where life is possible, life will be generated. Here it is suggested that the cause for a spontaneous generation of complex systems is probability driven processes. Based on equilibrium…
This paper aims to establish a central limit theorem for Markov processes conditioned not to be absorbed under a very general assumption on quasi-stationarity for the underlying process. To do so, a central limit theorem has been…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…
We derive an exact (classical and quantum) expression for the entropy production of a finite system placed in contact with one or several finite reservoirs each of which is initially described by a canonical equilibrium distribution.…
The essence of the second law of classical thermodynamics is the `entropy principle' which asserts the existence of an additive and extensive entropy function, S, that is defined for all equilibrium states of thermodynamic systems and whose…
We consider the problem of conditioning a Markov process on a rare event and of representing this conditioned process by a conditioning-free process, called the effective or driven process. The basic assumption is that the rare event used…
This paper studies a class of mixed mean-field jump processes on an abstract state space $\Pi$, together with their associated $N$-particle systems. The dynamics consist of the superposition of an independent Markovian component and a…
We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths beyond perturbation theory. Our approach is based on the exact time-local quantum master equation for the reduced open…
A generalization of the entropy production rate is proposed $\Pi_q$ in non-equilibrium systems by extending the formalism of classical stochastic thermodynamics to regimes with non-Gaussian fluctuations. Through the R\'enyi entropy $S_q$ ,…
We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
We establish a refined version of the Second Law of Thermodynamics for Langevin stochastic processes describing mesoscopic systems driven by conservative or non-conservative forces and interacting with thermal noise. The refinement is based…
The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic…
A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get a upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and…
A definition of the thermodynamic entropy based on the time-dependent probability distribution of the macroscopic variables is developed. When a constraint in a composite system is released, the probability distribution for the new…